Santos, who received the Nobel Peace Prize last month for his efforts to end Colombia's civil war, met May at 10 Downing St. On the second day of his three-day trip.
It's the first UK state visit by a Colombian leader, and is being used by UK officials to highlight Britain's international focus as it prepares to leave the European Union. Britons voted in June to leave the 28-nation bloc.
The energy deal announced today will see the two countries share information in areas such as regulation, supply-chain development and training.
May also announced a tax agreement with Colombia and 1 billion pounds (USD 1.2 billion) in export financing to encourage investment in rural health care and renewable energy projects.
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Yesterday, Santos and his wife Maria Clemencia Rodriguez de Santos dined on Dover sole and pot-roasted pheasant at a Buckingham Palace banquet hosted by Queen Elizabeth II.
Santos won the Nobel Prize for striking a deal with Colombia's main rebel group to end Colombia's long civil war, which has killed more than 200,000 people. But the peace pact with the Revolutionary Armed Forces of Colombia was narrowly rejected by voters.
May said Britain would support Colombia in its efforts to "secure a final and lasting peace agreement.